Title:Search for surface magnetic fields in Mira stars. First detection in chi Cyg

Abstract: In order to complete the knowledge of the magnetic field and of its influence
during the transition from Asymptotic Giant Branch to Planetary Nebulae stages,
we have undertaken a search for magnetic fields at the surface of Mira stars.
We used spectropolarimetric observations, collected with the Narval instrument
at TBL, in order to detect - with Least Squares Deconvolution method - a Zeeman
signature in the visible part of the spectrum. We present the first
spectropolarimetric observations of the S-type Mira star chi Cyg, performed
around its maximum light. We have detected a polarimetric signal in the Stokes
V spectra and we have established its Zeeman origin. We claim that it is likely
to be related to a weak magnetic field present at the photospheric level and in
the lower part of the stellar atmosphere. We have estimated the strength of its
longitudinal component to about 2-3 Gauss. This result favors a 1/r law for the
variation of the magnetic field strength across the circumstellar envelope of
chi Cyg. This is the first detection of a weak magnetic field at the stellar
surface of a Mira star and we discuss its origin in the framework of shock
waves periodically propagating throughout the atmosphere of these radially
pulsating stars. At the date of our observations of chi Cyg, the shock wave
reaches its maximum intensity, and it is likely that the shock amplifies a weak
stellar magnetic field during its passage through the atmosphere. Without such
an amplification by the shock, the magnetic field strength would have been too
low to be detected. For the first time, we also report strong Stokes Q and U
signatures (linear polarization) centered onto the zero velocity (i.e., at the
shock front position). They seem to indicate that the radial direction would be
favored by the shock during its propagation throughout the atmosphere.